| Title:
|
Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations (English) |
| Author:
|
Brestovanská, Eva |
| Author:
|
Medveď, Milan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
27-39 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the $m$-tuple Cartesian product of a Banach algebra $X$ over $\mathbb {R}$. Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved. (English) |
| Keyword:
|
fixed point |
| Keyword:
|
Banach algebra |
| Keyword:
|
integral equation |
| Keyword:
|
integro-differential system |
| Keyword:
|
epidemic model |
| Keyword:
|
blowing-up solution |
| MSC:
|
45G15 |
| MSC:
|
47B48 |
| MSC:
|
47H10 |
| MSC:
|
92D30 |
| idZBL:
|
Zbl 06204928 |
| idMR:
|
MR3058871 |
| . |
| Date available:
|
2012-11-26T10:15:25Z |
| Last updated:
|
2014-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143065 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[4] Bihari, I.: A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta Mathematica Hungarica 7, 1 (1956), 81–94. Zbl 0070.08201, MR 0079154, 10.1007/BF02022967 |
| Reference:
|
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| Reference:
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[6] Djebali, S., Hammache, K.: Furi-Pera fixed point theorems in Banach algebra with applications. Acta Univ. Palacki. Olomouc, Fac. Rer. Nat., Math. 47 (2008), 55–75. MR 2482717 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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[10] Olaru, I. M.: Generalization of an integral equation related to some epidemic models. Carpatian J. Math. 26 (2010), 0–4. Zbl 1224.34205, MR 2676722 |
| Reference:
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| . |
